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Running head: ACHIEVEMENT GAP PROJECT
Achievement Gap Project: The Relationship between Location, Income, and Achievement among African-American and At-Risk Students in Virginia
Roger S. Baskin, Sr.
Andre R. Marseille
George Mason University
Abstract
The purpose of this paper is to demonstrate our analysis of the variables of location, student income, and per-pupil expenditures in relation to achievement in math. Focused on school districts in the state of Virginia, the information gathered for this paper is extracted from sources including public demographic information provided by the Virginia Department of Education (2009) and The New America Foundation’s Federal Education Budget Project (2009).
Achievement Gap Project: The Relationship between Location, Income, and Achievement among African-American and At-Risk Students in Virginia
Introduction
A number of researchers have connected student achievement to the socioeconomic disparities that exist between the poor and the middle class (Kozol, 1991; Ladson-Billings, 2006; Lee & Burkam, 2002; Rothstein, 2004). Further, authors like Kozol (1991) point to the way schools are funded as a means of identifying contributing exacerbations to the inequity that exists between middle class and poor communities. Because of the popularity of this position, some educators resign themselves to the notion that nothing can be done to address disparities that exist because of the forces of poverty and economic disenfranchisement. The purpose of this paper is to demonstrate the degree to which this idea holds true in the state of Virginia when considered in light of urban, suburban and rural contexts. School districts from each demographic have been analyzed to demonstrate the degree to which poverty can explain math achievement.
The following questions will be pursued in this paper:
Q1: Is there a relationship between per-pupil expenditure and pass rates for economically disadvantaged students?
Q2: What is the relationship between math scores on the Virginia SOL’s in suburban and rural locations for African-American students?
Q3: What variables have the strongest relationship to math achievement for African-American students, location or per-pupil expenditures?
Methods
Design
Thirty school districts in the state of Virginia were randomly selected to participate in this study. The school districts represent urban, suburban, and rural contexts. State test scores in math were selected from the 2007-2008 school year.
Participants
Thirty school districts in the state of Virginia were selected for this study. Ten districts were considered to be urban because of the total number of students in the district, their percentage of students on free and reduced meals, and the amount of diversity within the district. Additionally, if the district is within a large inner city, it was identified as urban. In some cases, school districts were identified as urban although their geographic location may have been likened to suburban because of their demographics and size. Ten school districts in the study were identified as suburban because of their proximity to a large inner city. Ten school districts were identified as rural because of their geographic location in proximity to both inner city and suburban communities and their relative small size in comparison to urban and suburban communities.
Districts in the study ranged from various quadrants of the state of Virginia so as to select data that was representative of the entire state. This reduced the likelihood of the study being too focused on a particular region of the state.
Materials
Virginia report card of school districts.This database provides information concerning state test scores, pass rates, and historical data concerning test performance for all school districts and schools in the state of Virginia. We looked specifically at math pass rates for the 2007-2008 school year.
Federal education budget project.This database provides information concerning per-pupil expenditures for the 2005-2006 school year. Expenditures are calculated including such factors as educational supplies and technology.
Data Sources
Virginia math standards of learning test. In compliance with the No Child Left Behind Act (NCLB), the state of Virginia has developed this test as a way to measure student knowledge of math materials consistent with the program of study for the state. The test has approximately 50 multiple choice questions that measure math skills in the various grade levels. A passing score on the test is 400 which is about 56% correct answers. The score of 500 and above is pass-advanced. A perfect score is 600. The score was entered into the SPSS database by pass-rate percentage for the school district. Information is also included concerning pass rates for students labeled in the following ways on the Virginia Department of Education site: Black, White, Hispanic, At-risk. School districts ranged in overall pass rates from 73% to 92%.
Per-pupil expenditures. These records are taken from the 2005-2006 budgets of the schools and demonstrate the amount of money spent on teacher salaries, educational supplies. Transportation costs, building maintenance and other temporal costs are not associated with this figure. School districts ranged in per-pupil expenditures from $7,802 to $16,338.
Procedures
Information was gathered from the Virginia Department of Education website (2009) concerning student achievement data for the 2007-2008 Virginia Standards of Learning Mathematics Test. Information was gathered from The New America Foundation’s Federal Education Budget Project (2009) concerning per-pupil expenditures from 2005-2006.
School districts were identified in order to provide a balance of districts from urban, suburban, and rural settings as well as school districts that demonstrated regional diversity in terms of their geographic location. Following the identification of school districts to be used in the analysis, the results were analyzed using SPSS to determine the degree to which the variables of school expenditures, geographic, and test scores correlate. Diagnostic analysis of multiple regression was conducted to determine homoscedasticity, normality of residuals, linearity, multicollinearity, and outliers and influential data points.
Results
Chi square test of association.We conducted a Chi Square test of association to identify a possible association between pass rates for students that were FARM status and per-pupil expenditures. The Pearson chi-square value test statistic is 4.698. The X2 critical value for degrees of freedom is (R,3-1)(C,3-1)= 4. Hence, with df=4 and an alpha .05 level of significance, the critical value is 9.49. Thus we accept the Ha: because the chi-square test statistic does not exceed the critical value of 9.49.
SPSS also reports a p-value of (p =.320) associated with the X2 value. Since the p-value is greater than alpha .05, again, we accept the Ha: Thus, we concluded that there is a not a strong relationship between pass rate for FARM status students and per-pupil expenditures.
In addition, the standardized residuals show in all cells show no excessive contributors to the chi-square test statistic.
Multiple regression.We ran a multiple regression analysis to determine if the three selected predictors-location: Urban X7, Suburban X8 and Rural X9 accounted for a statistically significant proportion of the variance in Y (pass rates for African American students). A backward selection of predictors was conducted and revealed that variable X7 (urban) was not a significant enough contributor to Rsquare changed to the prediction of criterion variable Y and was eliminated, (X7, p=.?? greater than .05) The F-test in the ANOVA table shows that the F-statistic is not statistically significant. Thus, providing evidence that the variance in Y accounted for by the three predictors does equal zero for the population. Specifically, the coefficient of determination in the model summary table, Rsquare =.097, indicating that roughly 9% of the difference in African American pass rates are accounted for by location:
The multiple regression equation for predicting the dependent variable, Y(math scores), from X8 (location) and X9 (Race) is:
Based on the results, the X8 and X9 predictors did not have a statistically significant relationship to Y at p =.109, p =.254 respectively exceeding the alpha at .05. Neither predictors were unique contributors to Rsquare In other words, X8 and X9 do not statistically contribute to the variance in Y (African American pass rates). Looking at part correlations for X8 and X9, X8 =.303, or ry (1.2) =.303 squared = 9.1% of the variance in African American pass rates is uniquely accounted for by the variance in suburban locations. X9 part correlation is .219 or ry (2.1) =.219. .219 squared = 4.7% of the variance in African American pass rates in uniquely accounted for by rural location over and above the explanatory contribution of suburban.
To test the null hypothesis or Ho: Rsquared-pop =0, the sample size estimation of power for the predictors-X8 suburban and X9 rural at .95 for an R square of .25 and an alpha =.05 is R square = .25, .25/(1-.25) =0.3333, ES = 0.3333
n=L/ES +k+1, n=17.77/0.3333+2+1 =46.324+3, n= 54.515 or 55. Thus, a sample of 55 observations is necessary to reject the null hypothesis at the .05 level of significance, with a power of .95.
The results of the collinearity statistics indicate that there are no moderate to high correlations between the two predictors in the multiple regression analysis, hence multicollinearity is not an issue. VIFs for X8 and X9 are well below 10 at 1.333 each and tolerance is exact at .750 for both X variables which do not exceed the threshold of significance at 1.00. Residual statistics indicate a minimum/maximum range absolute value for SDRs is (-1.908 -+2.593) of which is less than 3.00, indicating no outliers on Y. The maximum value for Cook’s index is .185 which is less than 1.00 indicating that there are no influential data points. Leverage values range from .017 to .067 which is less than leverage established {3(2+1)/30 =0.3} indicating that there are no outliers on X.
Based on the “Normal P-Plot of Regression Standardized Residual” graph, visually, we can ascertain linearity between X and Y, because the observed and expected cumulative probabilities for standardized residuals stretches along the straight line. Regarding the assumption of homoscedastiscity, a scatter plot graph shows that dots are strategically plotted vertically indicating constant variance is present. A “Regression Standardized Residual” histogram shows a normal distribution indicating residual normality.
ANCOVA.We conducted an Ancova to determine if differences in math scores existed among African-American students living in rural, urban and suburban school districts. Per-pupil-expenditures was used as a covariate because it is an extraneous variable that does not indicate or explicitly or implicitly suggest any particular level of academic ability.
The Levene’s test of equality of error variances show that the assumption of homogeneity of variance is met, F(2, 27) = .52 is greater than .05. The test for the homogeneity of regression of slopes assumption is also met, F(1, 26) =1.03, p = greater than .05.
The F-test for African American math scores shows that any statistically significant differences among African American student math scores by location is undeterminable.
Discussion and Conclusions
Based on the analysis of the variables of location and per-pupil expenditures, there is no clear evidence to suggest that these variables impact math scores for African-American or at-risk students. We recommend looking more closely at the way in which the data is utilized in order to approach the question of correlation with greater certainty. We also recommend a larger sample size to identify a level of significance.
Reflection on the Process
Analyzing factors associated with achievement gaps requires a keen sense of both the systemic and individual issues that impact student achievement. The process demonstrated in this paper attempted to utilized a variety of quantitative methods to identify what some believe to be two contributing factors to persistent gaps in academic achievement among students of varying races and class—per-pupil expenditure and location of school district.
In order for results to yield a clear demonstration of impact and significance, the process has revealed the importance of identifying and carefully categorizing variables that have the greatest potential to unveil the sought after relationships. In this regard, being clear on the questions to be asked and on the factors to be analyzed is of most importance.
Additionally, this process demonstrates the constraints of quantitative approaches. Although beneficial in the analysis of larger samples, the quantitative approach still benefits from a balance with qualitative analyses that include interviews and case studies to demonstrate the living, breathing realities of phenomenon like the achievement gap.
A team approach, this process was also challenging in that it required the cooperation of two individuals with differing understandings of the topic and of the methods to approach the variables to be included in the analyses. The team approach was also beneficial in that it challenged both participants to come to grips with what the question really was that we were trying to get at and what was the best approach to further investigate the question. Primarily, it was beneficial to work on the project as a group because it demonstrated the kind of dialogue that needs to be had throughout the research community regarding such questions as the achievement gap and possible causes and solutions.
References
Kozol, J. (1991). Savage inequalities: Children in america’s schools. New York, NY:
HarperCollins.
Ladson-Billings, G. (2006). From the achievement gap to the education debt:
Understanding achievement in U.S. schools. 2006 Presidential address. Educational Researcher, 35 (7), pp. 3-12.
Lee, V. & Burkam, D. (2002). Inequality at the starting gate: Social
background differences in achievement as children begin school. Washington,
DC: Economic Policy Institute
Rothstein, R. (2004). Class and schools: Using social, economic, and educational
reform to close the black-white achievement gap. Washington, DC: Economic Policy Institute.
The New America Foundation (2009). Federal education budget project. Retrieved from
2009 from
Virginia Department of Education (2009). Virginia school report card. Retrieved from
Appendix A
Chi-Squared Test
Crosstabs
[DataSet0] C:\Documents and Settings\Owner\Desktop\Final Project for EDRS 811.sav
|Case Processing Summary |
| |Cases |
| |Valid |Missing |Total |
| |
| |
| |Value |df |Asymp. Sig. (2-sided)|
|Pearson Chi-Square |4.698a |4 |.320 |
|Likelihood Ratio |5.339 |4 |.254 |
|Linear-by-Linear Association |1.000 |1 |.317 |
|N of Valid Cases |30 | | |
|a. 7 cells (77.8%) have expected count less than 5. The minimum expected count is .13. |
Appendix B
Multiple Regression
REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA COLLIN TOL ZPP /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT Black /METHOD=ENTER Urban Suburban /PARTIALPLOT ALL /SCATTERPLOT=(*ZRESID ,*ZPRED) /RESIDUALS HIST(ZRESID) NORM(ZRESID) /SAVE COOK LEVER SDRESID.
Regression
|Variables Entered/Removed |
|Model |Variables Entered |Variables Removed |Method |
|1 |X8, X7a |. |Enter |
|a. All requested variables entered. |
|Model Summaryb |
|Model |R |R Square |Adjusted R Square |Std. Error of the |
| | | | |Estimate |
|1 |.311a |.097 |.030 |.04993 |
|a. Predictors: (Constant), X8, X7 |
|b. Dependent Variable: X1 |
|ANOVAb |
|Model |
|b. Dependent Variable: X1 |
|Coefficientsa |
|Model |
|Collinearity Diagnosticsa |
|Model |Dimension |Eigenvalue |Condition Index |Variance Proportions |
| |
|Residuals Statisticsa |
| |
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Second Test
REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA COLLIN TOL ZPP /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT Black /METHOD=REMOVE Urban Suburban /METHOD=FORWARD Rural /PARTIALPLOT ALL /SCATTERPLOT=(*ZRESID ,*ZPRED) /RESIDUALS HIST(ZRESID) NORM(ZRESID) /SAVE COOK LEVER SDRESID.
Regression
|Variables Entered/Removedd |
|Model |Variables Entered |Variables Removed |Method |
|1 |X9, X8a |. |Enter |
|2 |.b |X8c |Remove |
|a. Tolerance = .000 limits reached. |
|b. All requested variables entered. |
|c. All requested variables removed. |
|d. Dependent Variable: X1 |
|Model Summaryc |
|Model |R |R Square |Adjusted R Square |Std. Error of the |
| | | | |Estimate |
|1 |.311a |.097 |.030 |.04993 |
|2 |.071b |.005 |-.031 |.05146 |
|a. Predictors: (Constant), X9, X8 |
|b. Predictors: (Constant), X9 |
|c. Dependent Variable: X1 |
|ANOVAc |
|Model |
|b. Predictors: (Constant), X9 |
|c. Dependent Variable: X1 |
|Coefficientsa |
|Model |
|Excluded Variablesc |
|Model |
|b. Predictors in the Model: (Constant), X9 |
|c. Dependent Variable: X1 |
|Collinearity Diagnosticsa |
|Model |Dimension |Eigenvalue |Condition Index |Variance Proportions |
| |
|Residuals Statisticsa |
| |
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Appendix C
ANCOVA Tests
UNIANOVA Black BY Urban Suburban Rural WITH Money /METHOD=SSTYPE(3) /INTERCEPT=INCLUDE /SAVE=SRESID COOK LEVER /CRITERIA=ALPHA(.05) /DESIGN=Urban Suburban Rural Money.
Univariate Analysis of Variance
|Between-Subjects Factors |
| | |Value Label |N |
|X7 |.00 |.00 |20 |
| |1.00 |Urban |10 |
|X8 |.00 |.00 |20 |
| |2.00 |Suburban |10 |
|X9 |.00 |.00 |20 |
| |3.00 |Rural |10 |
|Tests of Between-Subjects Effects |
|Dependent Variable:X1 |
|Source |
UNIANOVA Black BY Urban Suburban Rural WITH Money /METHOD=SSTYPE(3) /INTERCEPT=INCLUDE /EMMEANS=TABLES(OVERALL) WITH(Money=MEAN) /EMMEANS=TABLES(Urban) WITH(Money=MEAN) /EMMEANS=TABLES(Suburban) WITH(Money=MEAN) /EMMEANS=TABLES(Rural) WITH(Money=MEAN) /EMMEANS=TABLES(Urban*Suburban) WITH(Money=MEAN) /EMMEANS=TABLES(Urban*Rural) WITH(Money=MEAN) /EMMEANS=TABLES(Suburban*Rural) WITH(Money=MEAN) /EMMEANS=TABLES(Urban*Suburban*Rural) WITH(Money=MEAN) /PRINT=ETASQ HOMOGENEITY /CRITERIA=ALPHA(.05) /DESIGN=Money Urban Suburban Rural Urban*Suburban Urban*Rural Suburban*Rural Urban*Suburban*Rural.
Univariate Analysis of Variance
|Between-Subjects Factors |
| | |Value Label |N |
|X7 |.00 |.00 |20 |
| |1.00 |Urban |10 |
|X8 |.00 |.00 |20 |
| |2.00 |Suburban |10 |
|X9 |.00 |.00 |20 |
| |3.00 |Rural |10 |
|Levene's Test of Equality of Error Variancesa |
|Dependent Variable:X1 |
|F |df1 |df2 |Sig. |
|.664 |2 |27 |.523 |
|Tests the null hypothesis that the error variance of the |
|dependent variable is equal across groups. |
|a. Design: Intercept + Money + Urban + Suburban + Rural + |
|Urban * Suburban + Urban * Rural + Suburban * Rural + Urban |
|* Suburban * Rural |
|Tests of Between-Subjects Effects |
|Dependent Variable:X1 |
|Source |
Estimated Marginal Means
|1. Grand Mean |
|Dependent Variable:X1 |
|Mean |Std. Error |95% Confidence Interval |
| | |Lower Bound |Upper Bound |
|.724a,b |.009 |.705 |.743 |
|a. Covariates appearing in the model are evaluated at the following |
|values: X5 (Dollars Per-Pupil) = 10413.2000. |
|b. Based on modified population marginal mean. |
|2. X7 |
|Dependent Variable:X1 |
|X7 |Mean |Std. Error |95% Confidence Interval |
| | | |Lower Bound |Upper Bound |
|.00 |.734a,b |.011 |.711 |.757 |
|Urban |.705a,b |.016 |.672 |.737 |
|a. Covariates appearing in the model are evaluated at the following values: X5 |
|(Dollars Per-Pupil) = 10413.2000. |
|b. Based on modified population marginal mean. |
|3. X8 |
|Dependent Variable:X1 |
|X8 |Mean |Std. Error |95% Confidence Interval |
| | | |Lower Bound |Upper Bound |
|.00 |.714a,b |.011 |.690 |.737 |
|Suburban |.745a,b |.017 |.711 |.779 |
|a. Covariates appearing in the model are evaluated at the following values: X5 (Dollars |
|Per-Pupil) = 10413.2000. |
|b. Based on modified population marginal mean. |
|4. X9 |
|Dependent Variable:X1 |
|X9 |Mean |Std. Error |95% Confidence Interval |
| | | |Lower Bound |Upper Bound |
|.00 |.725a,b |.012 |.701 |.749 |
|Rural |.722a,b |.017 |.687 |.757 |
|a. Covariates appearing in the model are evaluated at the following values: X5 |
|(Dollars Per-Pupil) = 10413.2000. |
|b. Based on modified population marginal mean. |
|5. X7 * X8 |
|Dependent Variable:X1 |
|X7 |X8 |Mean |Std. Error |95% Confidence Interval |
| |
|b. Based on modified population marginal mean. |
|c. This level combination of factors is not observed, thus the corresponding population marginal mean|
|is not estimable. |
|6. X7 * X9 |
|Dependent Variable:X1 |
|X7 |X9 |Mean |Std. Error |95% Confidence Interval |
| |
|b. Based on modified population marginal mean. |
|c. This level combination of factors is not observed, thus the corresponding population |
|marginal mean is not estimable. |
|7. X8 * X9 |
|Dependent Variable:X1 |
|X8 |X9 |Mean |Std. Error |95% Confidence Interval |
| |
|b. Based on modified population marginal mean. |
|c. This level combination of factors is not observed, thus the corresponding population marginal |
|mean is not estimable. |
|8. X7 * X8 * X9 |
|Dependent Variable:X1 |
|X7 |
|b. This level combination of factors is not observed, thus the corresponding population marginal mean is not |
|estimable. |
-----------------------
F(2, 27)=1.448, p = .253
Y=.019 X8 + .009 X9 + .703
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